Atomic quantum sensors for tes0ng general rela0vity ? W. Ertmer & E.M. Rasel IQ/LUH
Topics • detec0on and observa0on of gravita0onal waves, • test of the Lense‐Thirring effect, • test of the Weak Equivalence Principle.
Atom interferometer configura0on • detec0on and observa0on of gravita0onal waves: Phase meter, accelerometer • test of the Lense‐Thirring effect: Gyroscope • test of the Weak Equivalence Principle: Differen5al Accelerometer
Gravita0onal Waves
Strain in Space Curvature δ l • Abs. length varia0on δl increases with distance! • Free test bodies will change their rela0ve distance • Transversal waves
Gravita0onal Wave Sources Ground‐based detectors observe in the audio band • Space detectors observe low frequencies • Audio band 1 Hz – 10 kHz Gravity-gradient wall on the ground 6
GWD today and in future 10 -19 (a) 3 r d G eneration LIGO 2005 (b) LCG T (c ) adv anc ed LIG O 10 -20 (d) adv anc ed Virgo h(f) [1/sqrt(Hz)] (e) LIG O (f) Virgo 10 -21 (g) G EO 600 (g) (f) GEO-HF 10 -22 2009 (e) 10 -23 (a) (d) Ad LIGO/Virgo NB (b) Advanced LIGO/Virgo (2014) (c) 10 -24 Credit: M.Punturo Einstein GW Telescope 10 -25 1 10 100 1000 10000 Frequency [Hz] 7
The Third Genera0on The Einstein Gravita0onal Telescope E.T. • Overall beam tube length ~ 30km • Underground loca0on – Reduce seismic noise – Reduce gravity gradient noise – Low frequency suspensions • Cryogenic • Squeezing • QND Readout 8
Can atomic sensors contribute ?
Combining microscopic and macroscopic test masses
Drag‐free sensor |e 〉 〉 |g 〉 〉 5me Signal at the output ports S ∼ cos[( φ 3 ‐ φ 2 )‐( φ 2 ‐ φ 1 )] ( ) ΔΦ ≈ 2k eff hL sin ω GW T
Coherent Atomic Beam Spliier Posi0on Sensi0vity Mirror: Laboratory System periodicity G Fringe posi0on
Replacement of drag‐free sensor at lowest Fourier frequencies
averaging Scaling factor Averaging √T/ τ Atomic Temperature an issue and beam spliier velocity : T 2
Performance Noise limited sensi5vity GW‐ Sensors
Need for Femto‐g ONERA (2003) With cold atoms ?
∂ ϕ 2 2 2 ( ) ( ) /( ) ΔΩ = Δ ϕ ∂ Ω Increasing sensi6vity k ‐ large area Minimising phase noise Holger Müller (Berkeley): ‐ Increasing number of atoms Large area atom interferometry ‐ Bea0ng the shot noise ‐ Environmental control → Space ‐ Ultrastable lasers (frequency, intensity) Raman Laser
∂ ϕ 2 2 2 ( ) ( ) /( ) ΔΩ = Δ ϕ ∂ Ω Increasing sensi6vity k ‐ large area Minimising phase noise ‐ low frequency signal ‐ Increasing number of atoms long interac0on 0mes ‐ Bea0ng the shot noise → large atomic mass ‐ Environmental control → Space → Space ‐ Ultrastable lasers (frequency, intensity) ‐ ultra cold atoms ‐ Coherence Systema0cs Raman Laser
Seeking for Quantum Maier lowest temperatures in Microgravity
From Fountains to Large Facilities • Prototype experiments • 10m fountain or drop • Atom drop tower 100 m 10 m 1 m 22
Recent results: Evolu0on of the wave func0on Time-of-flight: 50, 100, 500 and 1000 ms
Recent results: Evolu0on of the wave func0on Time-of-flight: 50, 100, 500 and 1000 ms Evaporation over 1s 900 µ m 8000 - 10 000 atoms T < 10nK delocalised after 1s over 900 µ m
Back‐of‐enevelope es0mates for atomic phase meter ( ) ΔΦ ≈ 2k eff hL sin ω GW T • S/N limited resolu0on: 1 to 10 ‐2 mrad/√Hz Newtonian Noise • Scale factor for displacements: 1.6 10 ‐6 • Photon recoil, Mul0plica0on factor: 10‐100 to be combined with high S/N • Displacement sensi0vity: 10 ‐9 ‐10 ‐13 m • Length, Mul0plica0on Factor: 100‐1000 m • T ≅ 1‐10 s Strain sensi0vity 10 ‐13 ‐10 ‐16
detec0on and observa0on of gravita0onal waves on ground • Suspension „free“ gravita0onal wave detector • Sensi0vity iden0cal to light interferometer: „Phase meter“ • Newtonian Noise is fundamental barrier • Combining sensors at different Fourier frequencies (light and maier interferometer) • You need a pair of detectors for signal correla0on
detec0on and observa0on of gravita0onal waves on ground Many „Firsts“ to be demonstrated • High‐frequency source for ultracold (BEC) atoms (10Hz rate) • Combining high‐recoil beam spliiers with high phase resolu0on • Sub‐mrad resolu0on per shot • Novel microwave sources & ultra stable lasers • Control of systema0c errors • ...
detec0on and observa0on of gravita0onal waves in space • Control of drag‐free sensor at lowest Fourier frequencies • Replacement of the drag‐free sensor for measurements at lowest Fourier frequencies.
…with cold atoms Towards the limits Accelera5onal Sensi5vity with 10 8 ats: Microgravity 10 ‐12 g/ √ Hz @ Expansion Time 3 s Rota5onal Sensi5vity with 10 8 ats: Microgravity: 8 ⋅ 10 ‐12 rad/√Hz @ Expansion Time 3 s
Benefits of µ‐gravity environment Extended Time of Evolu6on Iner0al Quantum Sensors Rota0onal Phase ship Δ ϕ rot = 2 m Atom Ω ∝ T 2 Ω A ⋅ a Accellera0onal Phase ship Δ ϕ acc = T 2 k ⋅ a Sagnac Interferometer
Extended Time of Evolu6on Increase in sensi0vity kT 2 Rota0onal Phase ship Δ ϕ rot = 2 m Atom ∝ T 2 Ω A ⋅ Accellera0onal Phase ship Δ ϕ acc = T 2 k ⋅ a Transportable Cold Rubidium Sagnac Interferometer
CASI
CASI
Coherent beam splirng
Coherent beam splirng MIXER
Velocity selec0on
Rb Clock
Rota0on sensor 10 ‐8 rad/s√Hz
VLBI Resolu0on: The Earth‘s rota0on: 10 ‐8 – 10 ‐9 rad in Ω E ≈ 7,2∙10 ‐5 rad/s 24 h Rota0on sensing Applica0ons: ‐ Inves0ga0on of the Effects: Ω E Earth‘s rota0on Resolu0on: 10 ‐4 ‐ Geology 10 ‐9 rad in ‐ seismology 10 ‐5 1 year Gravity Probe B ‐ Star mo0on 10 ‐6 10 ‐7 ‐ Satellite naviga0on ‐ Tidal forces Resolu0on: 10 ‐8 ‐ Varia0on of the ‐ Rela0vis0c effects Earth‘s rota0on 10 ‐10 – 10 ‐11 rad/ 10 ‐9 ‐ … s √Hz ‐1 10 ‐10 ‐ Rela0vis0c Effects Ringlaser
Resolu0on: The Earth‘s rota0on: 10 ‐8 – 10 ‐9 rad in Ω E ≈ 7,2∙10 ‐5 rad/s 24 h Rota0on sensing Effects: Ω E 10 ‐4 ‐ seismology 10 ‐5 10 ‐6 10 ‐7 ‐ Tidal forces 10 ‐8 ‐ Varia0on of the Earth‘s rota0on 10 ‐9 10 ‐10 ‐ Rela0vis0c Effects
Perspec0ves Quantum sensors New atom interferometric • techniques are emerging Fundamental limits ? • GWD: Bringing free fall to earth • Atom‐light interferometer is the • most realis0c scenario Joint Ac0ons needed in order to proceed further for GAQS Gravita0onal Wave Atomic Quantum Sensor
ENOUGH SPACE FOR EXCITING EXPERIMENTS
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